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Assistant DirectorBrad Follmer and Agent John Doggett recognize Erwin Lukesh as he steps into the apartment building. They wait for him to check the mailbox for 4D while Agent Monica Reyes pretends to be repairing a bicycle while keeping track of the suspect. Follmer and Doggett watch via video camera in the surveillance van and when Lukesh walks away, they tell Reyes to be careful. She follows the man to a stairwell but losses track of him. She spins around just in time to get her throat cut by a blade.

Rushing in Doggett and Follmer find a dying Reyes on the stairs. Doggett goes after Lukesh as Follmer yells after him, “Doggett! He's got her gun!” Doggett easily catches the man, hands covered with blood, in the alley. As police arrive he looks away for just a moment to say, “Back here!” When he turns back around Lukesh has vanished. As he searches the alley, Lukesh appears behind Doggett. He turns to see Lukesh shoot him with Reyes' firearm.

Monica Reyes is unpacking in her new apartment. John Doggett arrives to deliver a housewarming gift. Polish sausage from the best place in the city. While Reyes goes to get plates, she receives a phone call for A.D. Walter Skinner. He tells her that they have found Doggett shot in an alleyway downtown. She says that is impossible as she steps into the other room to find no one there.

When she reaches the hospital, Reyes meets A.D. Brad Follmer and Agent Dana Scully. Scully says that if he pulls through he will be paralyzed. Reyes doesn't believe it was Doggett that was shot as he was with her in her apartment. They go into his room and there lies a severely injured Doggett being kept alive by machines.

After hearing Reyes once again state that Doggett was in the apartment, Scully relates the visitation by her dead father moments after his death. Reyes listens but flatly tells Scully that wasn't what happened to her. Walter Skinner calls and asks Scully and Reyes to go to the police station. Follmer awaits Reyes in the interrogation room.

Follmer asks her a few questions and tells her that the ballistics confirm her gun shot Agent Doggett. Reyes realizes that there is a witness behind the glass to identify her and she angrily yells at the glass. On the other side of the glass, Erwin Lukesh is thanked for his help in identifying the suspect. “Anything I can do to help.”

Skinner and Scully talk with Reyes at Doggett's bedside. They explain that Follmer will not arrest her yet because there are holes in his investigation, like how Skinner called her at home, 14 miles away from the crime scene. Additionally, the bullet matched her gun but her gun had not been fired recently. As Reyes asks about the witness, Doggett taps out a message with Morse code: LUKESH.

Erwin Lukesh returns home and makes the exact drink that his mother asks for before she asks for it. Pausing

briefly to spin Reyes' gun, Lukesh returns it to its drawer and delivers his paranoid needy bedridden mother her drink. He then goes to make her sandwich, taking out a plastic freezer bag containing a human tongue, while his mother chatters on ceaselessly in the other room.

Skinner tells Reyes that Erwin Lukesh claims to have heard a gun shot and found Reyes leaving the alleyway. Lukesh was diagnosed with a delusional disorder and spent four months in a sanitarium years ago. Reyes suggests that Doggett was investigating Lukesh. Follmer demands that Skinner bring Reyes to talk to Doggett at the hospital.

She goes in to see the injured man and Doggett explains through the computer that Lukesh killed her and tried to kill him. Elsewhere, Lukesh slips away in the night with his straight razor. The air shimmers around him as he disappears.

Reyes talks with Doggett about how she could be at a stakeout with him and he could be in her apartment with her at the same time. While Lukesh has no criminal record, Doggett claims he has killed many women and managed to escape every time somehow. Reyes theorizes that since Lukesh disappeared the second Doggett looked away, the man can somehow travel between parallel universes. This is how he got behind Doggett and how Doggett appeared here in this universe. He accidentally went through the portal. Going through pushed the Doggett of this universe into the other one.

In interrogation, Erwin Lukesh plays with Skinner and Follmer as they ask about the injured Doggett's claims that Lukesh enjoys killing women with a straight razor and cutting their tongues out. They try and convince him to submit to a gun-shot residue test but he refuses. When Skinner brings up the idea of the FBI going to speak with his mother, he gets extremely angry. He runs into Reyes on the way out and she confronts him about being able to switch between worlds. She suggests he needed a place where he could act out his sick fantasies but it couldn't be this world. All that anger needed a place to be expressed. He leans in close to Reyes and tells her how much he enjoyed killing her.

Erwin Lukesh's mother, Miriam Lukesh, has taken his gun from the drawer and asks him about it. She tells him

that the FBI has left several messages and that she will talk to them. Crying at the world, where he could pretend to be normal, shattering, Erwin Lukesh takes out his razor blade and kills his mother.

Back in the hospital, Doggett tells Reyes that he believes her theory and think if she pulls the plug, the other Doggett would return. She refuses to do it and suspects Doggett just wants to die. Skinner calls Reyes and informs her that they found Miriam Lukesh and that Erwin Lukesh may come after them now.

Follmer, Scully, and Skinner watch Reyes from the surveillance van. She patrols her apartment until Lukesh grabs her and puts the razor to her throat. He holds her just out of camera view and tells her, “This time, I get to bleed you slow.” Follmer bursts in and catches Lukesh with a round in the center of the forehead.

Reyes returns to Doggett's hospital room and holds his hand. She carefully turns off the alarms on the life

The title, "4-D", refers to an abbreviation of "fourth dimension". Time is generally accepted as being the fourth dimension, with length, breadth and height as the first three dimensions; the fifth dimension, a direction perpendicular to "the past" or "the future", is suggested as travel between parallel universes (so the title really should be "5-D"). The number is also the apartment number on the mailbox of the antagonist.

This episode is dedicated to the "Loving Memory" of Ricky Loyd Arreguin. According to the Associated Press, Ricardo Loyd Arreguin was a 16 year-old boy who was killed, with no apparent provocation, near a San Fernando Valley high school by Los Angeles gang members while walking home from school. Ricky's stepfather, Jose Arreguin, worked on props for The X-Files.